Vertical differential resonator

ABSTRACT

A micromechanical device includes a substrate, a micromechanical structure supported by the substrate and configured for overtone resonant vibration relative to the substrate, and a plurality of electrodes supported by the substrate and spaced from the micromechanical structure by respective gaps. The plurality of electrodes include multiple drive electrodes configured relative to the micromechanical structure to excite the overtone resonant vibration with a differential excitation signal, or multiple sense electrodes configured relative to the micromechanical structure to generate a differential output from the overtone resonant vibration.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. non-provisional applicationentitled “Vertical Differential Resonator,” now U.S. Pat. No. 8,878,633,filed Nov. 1, 2011, and assigned Ser. No. 13/294,950, which, in turn,claims the benefit of U.S. provisional application entitled “VerticalDifferential Resonator,” filed Sep. 27, 2011, and assigned Ser. No.61/539,912, the entire disclosures of which are hereby expresslyincorporated by reference.

BACKGROUND OF THE DISCLOSURE

1. Field of the Disclosure

The disclosure relates generally to micromechanical devices ormicro-electromechanical systems (MEMS) and, more particularly, tomicromechanical or MEMS resonators.

2. Brief Description of Related Technology

Micromechanical resonators have been constructed in accordance withso-called “free-free” designs. A free-free beam resonator contrastsfrom, for instance, a clamped-clamped beam resonator in which a resonantbeam is clamped, or anchored, at the ends of the beam. Free-free beamresonators are typically fabricated via surface micromachiningprocesses, vibrate in a direction vertically relative to the substrate,and exhibit good resonance performance for MEMS timing products.

Free-free beam resonator designs have utilized short support structures.Examples of free-free beam resonators with short support structures aredescribed in U.S. Pat. No. 6,930,569, the entire disclosure of which ishereby incorporated by reference.

Some free-free beam resonator designs have presented drawbacks inperformance, including inadequate power handling (or linearity) in whichthe output frequency varies at a level around −20 dBm. In contrast,quartz crystal resonators often operate at a level of 0 dBm.Improvements in power handling may lead to better phase noiseperformance of an oscillator driven by the resonator. As a result, MEMSoscillators have often exhibited worse phase noise than quartz crystaloscillators.

SUMMARY OF THE DISCLOSURE

In accordance with one aspect of the disclosure, a micromechanicaldevice includes a substrate, a micromechanical structure supported bythe substrate and configured for overtone resonant vibration relative tothe substrate, and a plurality of electrodes supported by the substrateand spaced from the micromechanical structure by respective gaps. Theplurality of electrodes include multiple drive electrodes configuredrelative to the micromechanical structure to excite the overtoneresonant vibration with a differential excitation signal, or multiplesense electrodes configured relative to the micromechanical structure togenerate a differential output from the overtone resonant vibration.

The micromechanical device may further include a plurality of supportstructures anchored to the substrate, each support structure beingcoupled to the micromechanical structure at a respective nodal point ofa set of nodal points of the micromechanical structure for the overtoneresonant vibration. In some embodiments, the plurality of supportstructures do not support the micromechanical structure at each nodalpoint of the set of nodal points. Alternatively or additionally, the setof nodal points includes supported nodal points and unsupported nodalpoints supported and not supported by a respective one of the pluralityof support structures, respectively. Alternatively or additionally, thesupported and unsupported nodal points are disposed in a symmetricalarrangement along the micromechanical structure. The symmetricalarrangement may then dispose each of the supported nodal points adjacentto one of the unsupported nodal points. Alternatively or additionally,the symmetrical arrangement includes matching locations of the supportedand unsupported nodal points on opposing sides of the resonantstructure.

In some embodiments, the overtone resonant vibration is a flexuralvibration mode. Alternatively or additionally, the overtone resonantvibration includes vibration in a direction transverse to the substrate.Alternatively or additionally, the micromechanical structure includes abeam configured for the overtone resonant vibration and spaced from theplurality of electrodes by the respective gaps. The beam may have acurved shape oriented in parallel with the substrate. The curved shapemay be annular.

In some cases, the overtone resonant vibration is at an overtoneresonant frequency for the 15th overtone of a fundamental resonantfrequency of the micromechanical structure.

The plurality of electrodes may include the multiple drive electrodesconfigured relative to the micromechanical structure to excite theovertone resonant vibration with the differential excitation signal andthe multiple sense electrodes configured relative to the micromechanicalstructure to generate the differential output from the overtone resonantvibration. The multiple drive electrodes and the multiple senseelectrodes may then be biased at different voltages relative to theresonant structure.

In some embodiments, the micromechanical structure includes a dielectriccore.

In accordance with another aspect of the disclosure, a micromechanicaldevice includes a substrate, a plurality of support structures anchoredto the substrate, a micromechanical structure supported by the substratevia the plurality of support structures and configured for overtoneresonant vibration relative to the substrate, the overtone resonantvibration having a set of nodal points along the micromechanicalstructure, and a plurality of electrodes spaced from the micromechanicalstructure by respective gaps, the plurality of electrodes includingmultiple drive electrodes configured to excite the overtone resonantvibration with a differential excitation signal, and further includingmultiple sense electrodes configured to generate a differential outputfrom the overtone resonant vibration. Each support structure of theplurality of support structures is disposed at a respective nodal pointof the set of nodal points. The micromechanical structure is notsupported at each nodal point of the set of nodal points by a respectiveone of the plurality of support structures.

In some embodiments, the plurality of support structures are disposed ina symmetrical arrangement along the micromechanical structure. Thesymmetrical arrangement may divide the set of nodal points into an equalnumber of supported and unsupported nodal points.

The overtone resonant vibration may be a flexural vibration mode.Alternatively or additionally, the overtone resonant vibration includesvibration in a direction transverse to the substrate. Alternatively oradditionally, the micromechanical structure includes a beam configuredfor the overtone resonant vibration and spaced from the plurality ofelectrodes by the respective gaps. The beam may have a curved shapeoriented in parallel with the substrate. The curved shape may beannular.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

For a more complete understanding of the disclosure, reference should bemade to the following detailed description and accompanying drawingfigures, in which like reference numerals identify like elements in thefigures.

FIG. 1 is a schematic, layout view of an exemplary micromechanicalresonator device configured for overtone resonant vibration anddifferential operation in accordance with one or more aspects of thedisclosure.

FIG. 2 shows a schematic, partial, perspective view of an exemplarymicromechanical resonator device during overtone resonant vibration inaccordance with one embodiment.

FIG. 3 is a schematic, partial, cross-sectional view of themicromechanical resonator device of FIG. 2 taken along lines 3-3 of FIG.2.

FIG. 4 shows a schematic, partial, perspective view of an exemplarymicromechanical resonator device during overtone resonant vibration inaccordance with another embodiment having one or more missing supportstructures.

FIG. 5 is a schematic, partial, cross-sectional view of themicromechanical resonator device of FIG. 4 taken along lines 5-5 of FIG.4.

FIG. 6 is a graphical plot depicting the operational performance of theexemplary micromechanical resonator device of FIG. 4.

FIGS. 7 and 8 are schematic, layout views of exemplary micromechanicalresonator devices configured for differential operation at seventh andthird overtones of a fundamental frequency in accordance withalternative embodiments, respectively.

FIGS. 9A-9D are graphical plots depicting the performance of a free-freeshort support micromechanical resonator device configured for operationat a 15th overtone frequency of 18 MHz in accordance with oneembodiment.

FIGS. 10A-10D are graphical plots depicting the performance of afree-free short support micromechanical resonator device configured foroperation at a 15th overtone frequency of 64 MHz in accordance with oneembodiment.

FIG. 11 is a schematic, partial, perspective view of an exemplarymicromechanical resonator device having an annular micromechanicalstructure configured for overtone resonant vibration and differentialoperation in accordance with one embodiment.

FIG. 12 is a graphical plot depicting the performance of themicromechanical resonator device of FIG. 11.

FIG. 13 is a schematic, partial, perspective view of another exemplarymicromechanical resonator device having an annular micromechanicalstructure configured for overtone resonant vibration and differentialoperation at an overtone frequency of 1.4 MHz.

FIG. 14 is a graphical plot depicting the performance of themicromechanical resonator device of FIG. 13.

While the disclosed devices are susceptible of embodiments in variousforms, there are illustrated in the drawing (and will hereafter bedescribed) specific embodiments of the invention, with the understandingthat the disclosure is intended to be illustrative, and is not intendedto limit the invention to the specific embodiments described andillustrated herein.

DETAILED DESCRIPTION OF THE DISCLOSURE

The disclosure relates to high performance MEMS resonator designs. Thedisclosed resonators may be useful in a variety of timing andcommunication applications. In one aspect, the disclosure relates toMEMS or other micromechanical resonator devices configured fordifferential operation. The differential operation may be fullydifferential. As described below, the fully differential resonators mayaccordingly include a number of electrodes in multiples of four (e.g.,positive input, negative input, positive output, negative output). Insome embodiments, the differential operation includes a single-endedinput or a single-ended output. Alternatively or additionally, thedisclosure relates to micromechanical resonator devices configured forhigh mode, overtone operation. In fully differential embodiments, theovertone mode may accordingly be one of the overtones in the 2^(n)−1sequence, e.g., third, seventh, 15th, 31^(st), etc.

In some embodiments, the disclosed micromechanical resonator devices areconfigured for resonant vibration at an overtone of a fundamentalresonant frequency of the micromechanical resonator device. Suchovertone resonant vibration provides multiple electrode locations, whichmay be suitable for developing non-inverting and inverting outputsignals. Multiple electrode locations may also be provided fordifferential inputs via such overtone resonant vibration, therebysupporting fully differential operation.

In another aspect of the disclosure, the micromechanical resonatordevice is not supported at each nodal point established during theovertone resonant vibration. A micromechanical structure of theresonator device configured for the overtone resonant vibration may besupported by a number of support arms or other structures, each one ofwhich is disposed at a respective nodal point of the overtone resonantvibration. In some embodiments, one or more nodal points may be missinga support structure. For example, the support arms may be skipped atevery other nodal point, and/or the support arms may be aligned with oneanother in a laterally symmetrical arrangement. A variety of symmetricalarrangements of the support structures may be used (e.g., a supportstructure at every third nodal point).

The disclosed resonators may exhibit improved power handlingcharacteristics. For example, the disclosed resonators may exhibitlinearity at levels equal to those of quartz crystal resonators. Thehigh mode and/or other aspects of the disclosed resonators may lead tothese operational improvements.

The disclosed resonator designs may avoid the limitations ofsingle-ended MEMS resonators. Because MEMS resonators are typicallysmall, the size of an electrode is very small. The disclosed resonatordesigns address the difficulty of building a MEMS resonator withmultiple electrodes with 180 phase difference for differential resonatoroperation. The differential operation of the disclosed resonators maylead to decreased sensitivity to electromagnetic interference.

The disclosed resonator designs may address limitations on operationalfrequency. The size of drive/sense electrode(s) of a typical free-freebeam resonator often decreases with higher operating frequencies of theresonator. As a result, the motional impedance is often high for highfrequency resonators. The overtone operation of the disclosed resonatordevices may address this challenge.

In some embodiments, the disclosed devices include a higher modeovertone free-free beam resonator with short support structures. Eachsupport structure may include a beam-shaped arm coupling the resonantstructure to respective substrate anchors. The support structures areplaced at the nodal points for a high overtone mode shape.

The micromechanical structure configured for resonant vibration may alsobe beam-shaped. The beam shape may be curved to any desired extent. Forexample, the micromechanical structure may be annular.

Although described in connection with a number of examples of free-free,short support resonator devices, one or more aspects of the disclosureare applicable to other types of micromechanical resonator devices. Theresonator devices need not be disposed in a free-free configuration. Thelength and other characteristics of the support structures may vary fromthe examples described. Other aspects of the devices may vary as well,including, for instance, the orientation of the vibration mode and/orthe type of vibration mode. For example, one or more aspects of thedisclosure may be applied to lateral vibration mode deviceconfigurations, and one or more aspects of the disclosure may be appliedto bulk acoustic mode devices configurations.

FIG. 1 shows an exemplary MEMS resonator device 20 constructed inaccordance with one embodiment. The device 20 includes a substrate 22 onwhich one or more electrodes 24 and a number of anchors 26 are disposedand/or by which the electrode(s) 24 and the anchor(s) 26 are supported.The anchors 26, in turn, support a resonant structure 28 in acantilevered, suspended, or other spaced position relative to thesubstrate 22 and the electrode(s) 24. The resonant structure 28 may be asurface micro-machined, bulk micro-machined or other micromechanicalstructure. The resonant structure 28 is supported by the substrate 22(e.g., via the anchors 26) and configured for resonant vibrationrelative to the substrate 22 in a gap 29 (FIG. 3) between theelectrode(s) 24 and the resonant structure 28. To that end, the resonantstructure 28 may include one or more conductive materials, surfaces,and/or regions for electrostatic excitation. As described below, theresonant vibration may include overtone resonant vibration.

The resonant structure 28 may be biased at a DC voltage V_(p) relativeto the electrode(s) 24. The bias voltage Vp may be used to pull down orotherwise draw the resonant structure 28 toward the electrode(s) 24 topromote vibration, increase stiffness, resonant frequency, etc. Theexcitation of the resonant structure 28 results in vibration at afundamental (or other) resonant frequency of the resonant structure 28.The DC bias voltage may be applied to the resonant structure 28 via oneor more of the anchors 26. In this example, the bias voltage isestablished by tying one or more of the anchors 26 (e.g., outermostanchors) to ground as shown, and by biasing the electrodes 24 at one ormore voltage levels relative to ground. In the example of FIG. 1, twodifferent bias voltages are established, V_(p-input) and V_(P-output),by applying different voltages to the electrodes 24 based on whether theelectrodes 24 are directed to input or output functions. Thus, half(e.g., eight) of the electrodes 24 may be tied to V_(p-input), and theother half (e.g., eight) of the electrodes 24 may be tied toV_(P-output). The arrangement of different bias voltages may provideflexibility during operation. For example, the different bias voltagesmay allow the resonator operating point of the device 20 to be tuned. Inone embodiment, a lower V_(p-input) (e.g., relative to the other biasvoltage) may be used to send more drive voltage into the resonantstructure 28. Alternatively or additionally, a higher V_(P-output)(e.g., relative to the other bias voltage) may be used to increaseoutput current. Such bias voltage arrangements may lead to improvedpower handling.

In this example, the resonant structure 28 is driven differentially viaan AC input or drive signal v_(i) applied to one or more positive (ornon-inverted) drive or input electrodes 30 and an inverted drive signal−v_(i) applied to one or more negative (or inverted) drive or inputelectrodes 32. Together the non-inverted and inverted drive signals areapplied to the drive electrodes 30, 32 to excite the resonant structure28 into vibration. Each drive electrode 30, 32 is positioned to drivethe resonant structure 28 into resonant vibration via the drive signals.In this example, each drive electrode 30, 32 includes a number offinger-shaped strips or other component structures 34 disposed on orotherwise above the substrate 22 and yet under the resonant structure28. Each finger-shaped strip 34 may be spaced from the resonantstructure 28 by the gap 29 (FIG. 3). Each finger-shaped strip 34 mayextend across a width of the resonant structure 28 as shown, but thelength, shape, and other characteristics of this component or section ofthe electrodes 30, 32 may vary from the example shown. Each strip 34 maybe considered a separate electrode of the drive electrodes 30, 32.Viewed in that way, the resonator device 20 includes four positive driveelectrodes and four negative drive electrodes. More generally, themultiple drive electrodes 30, 32 are configured relative to the resonantstructure 28 to excite the resonant vibration (e.g., overtone resonantvibration) with a differential excitation signal.

The example of FIG. 1 is configured as a fully differential resonatordevice. The output of the device 20 is sensed differentially by one ormore positive or non-inverting sense electrodes 36 as a sense current i₀and by one or more negative or inverting sense electrodes 38 as a sensecurrent −i₀. The output of the disclosed devices may alternatively oradditionally be sensed as a voltage. Each sense electrode 36, 38 ispositioned to sense the resonant vibration of the resonant structure 28.In this example, each sense electrode 36, 38 includes a number offinger-shaped strips or other component structures 40 disposed on orotherwise above the substrate 22 and yet under the resonant structure28. Each finger-shaped strip 40 may be spaced from the resonantstructure 28 by the gap (FIG. 3). Each finger-shaped strip 40 may extendacross a width of the resonant structure 28 as shown, but the length,shape, and other characteristics of this component or section of theelectrodes 36, 38 may vary from the example shown. Each strip 40 may beconsidered a separate electrode of the sense electrodes 36, 38. Viewedin that way, the resonator device 20 includes four positive senseelectrodes and four negative sense electrodes. More generally, themultiple sense electrodes 36, 38 are configured relative to the resonantstructure 28 to generate a differential output from the resonantvibration (e.g., overtone resonant vibration). In other embodiments, theelectrodes 24 may be configured for either single-ended excitation orsingle-ended output. In the former case, the electrodes 24 include thepositive and negative input electrodes 30, 32, as described above, butonly a single output signal is captured. In the latter case, theelectrodes 24 include the positive and negative output electrodes 36,38, but only a single input signal is applied to excite the device 20.

The resonant structure 28 may be coupled to the anchors 26 via a numberof support structures 42, which may be configured as arms extendingbetween the anchors 26 and the resonant structure 28. The supportstructures 42 are thus anchored to the substrate 22. For example, eachsupport structure 42 may be a beam-shaped arm that couples the resonantstructure 28 to one of the anchors 26. Each support structure 42 in thisexample is attached to the resonant structure 28 at respective nodalpoint of a set of nodal points of an overtone mode of the fundamentalresonant frequency of the resonant structure 42. Resonance at theharmonic frequency of the overtone mode is established during operationvia application of the drive signals at appropriate positions along theresonant structure 28. As described below, the resonant structure 28 maybe configured to resonate at various harmonics of the fundamentalresonant frequency of the resonant structure 28. The example of FIG. 1is configured to resonate at an overtone resonant frequency for the15^(th) overtone, or 16^(th) harmonic frequency, of the fundamentalresonant frequency of the resonant structure 28.

The support structures 42 may be disposed in a symmetrical arrangement.In this example, the symmetry is lateral, e.g., across the width of theresonant structure 28. Each support structure 42 on one side of theresonant structure 28 is aligned with a corresponding one of the supportstructures 42 on the opposing side of the resonant structure 28. Thearrangement is also symmetrical along the other lateral dimension of theresonant structure 28, e.g., across the length of the resonant structure28. The support structures 42 are symmetrical about a center linepassing through center support structures 44. These lateral symmetriesmay also be exhibited in other support structure arrangements describedherein.

The resonator device 20 has a free-free configuration in the sense thatthe resonant structure 28 is supported and spaced from the substrate 22and the electrodes 24 with free ends 44 as opposed to clamped orotherwise fixed ends. The free-free resonator configuration may minimizelosses to the substrate 22, but other embodiments may include one ormore clamped or fixed ends. The example of FIG. 1 may further minimizesuch losses by designing the support structures 42 to have a lengthselected in view of the harmonic frequency of the overtone mode. Forexample, each support structure 42 may have a length substantially lessthan a quarter-wavelength of the harmonic frequency. Further detailsregarding such short support arms are set forth in U.S. Pat. No.6,930,569 (“Micromechanical resonator having short support arms”), theentire disclosure of which is incorporated by reference. Notwithstandingthe advantages of short support arms, one or more of the supportstructures 42 may be alternatively configured with, for instance, alength equal to a quarter-wavelength.

In this example, the resonant structure 28 is beam-shaped for a flexuralmode of vibration. The vibration mode primarily includes movement in adirection vertical or transverse to the plane of the substrate 22. Theelectrodes 24 and the resonant structure 28 may thus be orientedrelative to one another for vibration of the resonant structuretransverse to the substrate 22. In other examples, the flexural mode ofvibration includes movement in a direction lateral or parallel to theplane of the substrate 22. The vibration mode need not be flexural andinstead may be based on movement involving, for instance, expansion andcontraction of the resonant structure 28. Thus, the vibration mode maybe a bulk acoustic mode.

The above-described components of the device 20 may be formed viasurface micromachining fabrication techniques, examples of which aredescribed below. The electrodes 24 and the anchors 26 may be made ofpolysilicon or other conductive materials. The polysilicon regions ofthe structures may be doped (e.g., n-type or p-type) to a dopantconcentration sufficient to reach a desired conductivity level. Theanchors 26 may be integrally formed with the resonant structure 28,which may thus include polysilicon as well.

The device 20 may include varying numbers of electrodes and anchors. Inthis example, the device 20 includes one or more outer electrodes 46biased at the same voltage (e.g., ground) as the resonant structure 28.The outer electrodes 46 are disposed under lateral ends of the resonantstructure 28 to prevent the resonant structure from contacting duringvibration a structure or layer (e.g., a nitride layer) disposed at adifferent voltage (e.g., a floating or otherwise uncontrolled voltage).With the outer electrodes 46 and the resonant structure 28 disposed atthe same voltage, any such contact is not problematic. The electrodes 46may also provide mechanical balance for the device 20. The shape, size,positioning, and other characteristics of the electrodes and anchors mayvary considerably from the example shown. For example, the device 20need not have integrated electrodes branching out from a commonterminal, and instead may be configured with non-integrated sense anddrive electrodes spaced from the resonant structure 28. The device 20may also include any number of such distinct or discrete senseelectrodes, and any number of such distinct or discrete driveelectrodes. The structural support, bias, and excitation framework andarrangement of the device 20 may vary considerably from the exampleshown.

In some cases, the substrate 22 may include a silicon or othersemiconductor base, or original substrate, along with various types ofsemiconductor, insulating, or other layers, such as epitaxial layers,formed thereon. The electrodes 24, the anchors 26, and other componentsof the device 20 need not be disposed directly on the substrate 22, andinstead may be supported indirectly by the substrate 22 via any numberof such intervening layers.

Further details regarding the device 20, one or more of its constituentstructures, and/or the fabrication of the device 20 and/or itsconstituent structures may be found in the above-referenced U.S. Patent,as well as U.S. Pat. No. 6,249,073 (“Device including a micromechanicalresonator having an operating frequency and method of extending same”),the entire disclosure of which is incorporated by reference. The device20 may include one or more components directed to temperaturecompensation, the techniques of which may be applied either separatelyor in combination with one or more other temperature compensationtechniques (e.g., mechanical, electrical, oven-based, etc.), such asthose described in U.S. Patent Publication No. 2002/0069701(“Micromechanical resonator device”) and U.S. Pat. No. 7,449,968(“Frequency and temperature compensation synthesis for a MEMSresonator”), the entire disclosures of which are incorporated byreference.

The device 20 is shown in schematic form in FIG. 1 and the other drawingfigures hereof for convenience in illustration, and may include a numberof other components in certain applications or operationalconfigurations. For example, the lateral and other dimensions of thestructures depicted in FIG. 1 may be exaggerated and out of scale forease in illustration. As shown and described herein, the shape, size,and other characteristics of the resonant structure 28 may varyconsiderably from the beam-shaped example of FIG. 1. For example, theresonant structure 28 need not be made of polysilicon. In some cases,the resonant structure 28 includes a dielectric or other temperaturecompensating core as described in U.S. patent application Ser. No.11/315,436 (“Temperature Compensated Resonator with Dielectric Core”),the entire disclosure of which is incorporated by reference. The shapeand other characteristics of the resonant beam may also vary from theexample of FIG. 1, as shown and described in connection with the curvedbeam example of FIG. 11. The differential operation, overtone mode, andother aspects of the disclosure may be incorporated into a wide varietyof resonant structures with any manner of structural complexity (e.g.,trusses, shuttles, multiple beam construction, etc.).

FIGS. 2 and 3 show another exemplary micromechanical resonator device 50configured in accordance with one or more aspects of the disclosure. Thedevice 50 is illustrated during operation in a flexural overtoneresonant mode. The device 50 includes a resonant structure 52 supportedby anchors 54 (FIG. 2) in a free-free resonator configuration. In thisexample, the overtone resonant mode is a vertical flexural mode at the7^(th) overtone (8^(th) harmonic) of the fundamental resonant frequencyof the resonant structure 52 with each of the anchors 54 disposed atnodal points of the overtone resonant mode. The resonant structure 52may be considered beam-shaped, despite both lateral dimensions of thestructure 52 being greater than the thickness of the structure 52.

The 7^(th) overtone resonant mode is excited by a number of driveelectrodes 56 (FIG. 3). As with the example of FIG. 1, the resonatordevice 50 is configured for fully differential operation. The driveelectrodes 56 include both positive and negative electrodes. Thisexample includes two positive drive electrodes and two negative driveelectrodes. The overtone resonance of the device 50 is captured by anumber of sense electrodes 57, half of which are positive (ornon-inverting) and half of which are negative (or inverting). Theresonator device 50 may nonetheless be configured for differentialoperation in which either the input or the output electrodes 56, 57 aresingle-ended. Each of the drive and sense electrodes 56, 57 is disposedat a position along the resonant structure 52 of maximum displacementduring the overtone resonant vibration, as best shown in FIG. 3.

The resonant structure 52 is spaced from a substrate (FIG. 1) and theelectrodes 56 by respective gaps 29 (FIG. 3). The resonant structure 52is supported by the substrate via the anchors 54. The resonant structure52 is coupled to the anchors via a number of support structures 58. Theresonant structure 52 is configured for overtone resonant vibrationrelative to the substrate. The overtone resonant vibration has a set ofnodal points. Each support structure 58 is positioned along the resonantstructure 52 at a respective one of the nodal points of the overtoneresonant mode. In this example, each nodal point has a respective one ofthe support structures 58, as best shown in FIG. 3.

The support structures 58 are disposed in a symmetrical arrangementsimilar to the arrangement described above in connection with theexample of FIG. 1.

FIGS. 4 and 5 show another micromechanical resonator device 60 duringoperation in an overtone resonant mode. The device 60 may vibrate at thesame mode shape (e.g., the 7^(th) overtone mode) as that described abovein connection with the example of FIGS. 2 and 3. The overtone resonantvibration and differential operation of this embodiment may be similarin other respects to the examples described above. For example, theresonator device 60 may include a similar electrode arrangement havingthe drive/sense electrodes 56 disposed and configured as described abovein connection with the example of FIGS. 2 and 3. The resonator device 60differs from the above-described devices in that a resonant structure 62of the device 60 is not supported at each nodal point of the overtoneresonant mode. The resonator device 60 is shown in FIG. 5 with areference line 64 indicating the locations of the nodal points. In thisexample, the resonator device 60 has a support structure 66 at everyother nodal point. Skipping every other nodal point may minimize lossesinvolving the support structures 66 and anchors 68 that support theresonant structure 62 above the substrate via the support structures 66.

More generally, the micromechanical structures of the disclosed devicesneed not be supported at each nodal point of the set of nodal points bya respective one of the plurality of support structures. That is, insome embodiments, the support structures of the disclosed devices do notsupport the micromechanical structure at each nodal point of the set ofnodal points of the resonant mode. Thus, the set of nodal points mayinclude supported nodal points 70 and unsupported nodal points 72supported and not supported by a respective one of the plurality ofsupport structures 66, respectively. In this example, every other nodalpoint is skipped along each side of the resonant structure 62.

The support structures 66 and, thus, the supported and unsupported nodalpoints 70, 72, may be disposed in a symmetrical arrangement along themicromechanical structure 62. In this example, the arrangement is againsymmetrical in the lateral dimensions, as described above. The exemplarysymmetrical arrangement includes matching or aligning locations of thesupported and unsupported nodal points 70, 72 on opposing sides 74, 76of the resonant structure 62. The other lateral symmetry is about theline passing through the two support structures 66 disposed in themiddle of the resonant structure 62. The symmetrical arrangement of thisexample also disposes each of the supported nodal points 70 adjacent toone of the unsupported nodal points 72.

The above-described support structure arrangements may lead to multipleperformance improvements. For example, FIG. 3 depicts the resonantspectrum of the exemplary embodiment of FIG. 1. The quality factor, Q,of the device is 14,010. Other operational parameters of the resonatordevice include an overtone resonant frequency of 70 MHz, a motionalimpedance of 10 kΩ, and a bias voltage of 1.4V. Resonator devices (suchas the device 20 of FIG. 1) configured for operation at the 15^(th)overtone may exhibit such superior performance because the increasednumber of electrodes may lower the motional impedance. As a result, theresonators may operate with a lower bias voltage. Further operationalimprovements regarding, for instance, power handling are describedbelow.

The quality factor and other performance characteristics of the otherabove-described embodiments are not adversely affected by skipping oneor more support structures 66, as described above. In fact, lowering thenumber of support structures 66 may help improve one or more of theperformance characteristics. One or more lateral or other symmetries ofthe support structure arrangement may also help maintain theseoperational improvements at the overtone resonant mode.

Notwithstanding these performance improvements, the disclosed devicesmay use other support structure arrangements in alternative embodiments,including, for instance, skipping two support structures for everysupported nodal point, or supporting two support structures for everyunsupported nodal point. Embodiments without missing support structuresmay also exhibit symmetry in the support structure arrangement. Forexample, the resonator device 20 of FIG. 1 has the support structuresdisposed in a lateral symmetrical arrangement. In that case and otherembodiments, the positions of the support structures on opposing sidesare aligned.

A variety of differential resonator device designs may be supported bythe high overtone mode of the disclosed resonator devices. As shown inthe examples of FIGS. 1-5, the differential resonator devices may have16 electrodes, in which four electrodes are configured for positivedrive, and another four electrodes are configured for negative drive.The remaining eight electrodes include another four electrodesconfigured for positive sensing, and the remaining four electrodesconfigured for negative sensing. Other fully differential resonatordevices constructed in accordance with the disclosure may be configuredfor operation at the third overtone (fourth harmonic) and seventhovertone (eighth harmonic). Examples of such resonators are shown inFIGS. 7 and 8.

FIG. 7 depicts an exemplary resonator device 80 that may be configuredfor fully differential operation and resonance at the third overtone ofthe fundamental resonant frequency of a resonant structure 82. Thedevice 80 includes four electrodes 84, each one of which may bededicated to a discrete drive/sense function (e.g., positive andnegative inputs and positive and negative outputs). The resonantstructure 82 is supported by a substrate via a plurality of anchors 86and support structures 88 coupling the anchors 86 to the resonantstructure 82. The support structures 88 may be arranged symmetrically asdescribed above. For example, the symmetry may include lateral alignmentacross the width of the resonant structure 82 and lateral symmetry abouta center line passing through center support structures 90).

FIG. 8 depicts another exemplary resonator device 100 that may beconfigured for fully differential operation. In this example, the device100 is configured for resonance at the 7^(th) overtone of thefundamental resonant frequency of a resonant structure 102. The device100 includes eight electrodes 104, with pairs of the electrodes 104dedicated to respective drive/sense functions. For example, theelectrode pairs may be arranged in a manner similar to the groups offour electrodes described above in the example of FIG. 1. The device 100may be otherwise configured similarly to the examples of FIG. 1 and FIG.7.

Notwithstanding the foregoing examples, the disclosed resonator devicesneed not be configured for fully differential operation. For example,and as shown in the graphical plots described below, the discloseddevices may be configured with a single-ended input and differentialoutputs.

FIGS. 9A-9D are graphical plots depicting the performance of a free-freeshort support resonator device configured for operation at a 7^(th)overtone of 18 MHz with a single-ended input and differential output,but otherwise in accordance with the example described above inconnection with FIGS. 4 and 5. FIG. 9A depicts the frequency spectrumand phase response of the resonator device. FIG. 9B depicts the qualityfactor, Q, and motional impedance as a function of bias voltage. FIG. 9Cdepicts the sensitivity of the operational frequency (i.e., the harmonicfrequency) of the device as a function of bias voltage. FIG. 9D shows animprovement in power handling (e.g., about 10 dB) during operation offour samples of such 18 MHz devices.

FIG. 10A-10D are graphical plots depicting the performance of afree-free short support resonator device configured for operation at an15^(th) overtone of 64 MHz with a single-ended input and differentialoutput, but otherwise in accordance with the example described above inconnection with FIGS. 4 and 5. FIG. 10D shows an improvement in powerhandling (e.g., over about 20 dB) during operation of the 64 MHz deviceat varying bias voltages. The improvement also includes an upwardfrequency shift that may be useful in offsetting an opposite frequencyshift that arises from a non-linear electrostatic effect of theresonator device design. The upward frequency shift shown in FIG. 10Dmay arise from a mechanical non-linearity arising from the operation atthe overtone resonant mode.

The operational performance of the above-described high mode overtonefree-free beam resonators with short support structures exhibited highquality factor levels, while exhibiting power handling levels at 0 dBm,the same level as quartz crystal resonators.

FIG. 11 depicts another example of a resonator device 110 configured foroperation at an overtone resonant mode. The resonator device 110includes a beam-shaped resonant structure 112 configured for flexuralvibration, as described above. The resonator device 110 may still beconsidered a free-free beam resonator, as the “ends” of the beam remainfree of any clamp. In this example, the beam of the resonant structure112 has a curved shape rather than a rectilinear one. The curve of theresonant structure 112 is oriented in parallel with the substrate suchthat the vibration remains vertical, or transverse relative to thesubstrate as shown. In this example, the curve of the resonant structure112 forms a ring or annular shape. The curve of the resonant structure112 may vary from the example shown, insofar as the resonant structureneed not be bent to an extent that the ends thereof meet to form a ringas shown. Instead, the resonant structure 112 may have a semi-annularshape, with, for instance, the ends being disposed proximate to oneanother.

The resonator device 110 may include any number of anchors 114 andcorresponding support arms or other structures 116. One or more of thesupport structures 116 may be skipped as described above. The resonatordevice 110 may include any number of electrodes (not shown) to supportsingle-ended, partially differential, or fully differential operation.The electrodes may be dedicated to a particular drive or sense function(e.g., positive or negative inputs or outputs). Alternatively, one ormore of the electrodes may be configured as a drive/sense electrode asdescribed above.

FIG. 12 depicts the performance of the ring-shaped resonator of FIG. 11.The quality factor, Q, of the ring-shaped resonator is about twice thelevel of current devices.

FIG. 13 depicts another ring-shaped overtone resonator device 120configured for overtone resonant vibration at 1.4 MHz. The resonatordevice 120 may be configured similarly in one or more aspects to theabove-described devices, including a beam-shaped resonant structure 122bent into an annular configuration. In this embodiment, however, theresonant structure 122 has a non-uniform width. In this example, thenon-uniform width of the resonant structure 122 is provided by a numberof lateral projections 124. Each projection 124 adds mass to theresonant structure 124, which may reduce the fundamental and otherresonant frequencies of the device 120. The projections 124 need not beshaped as beams or bars oriented transversely to the main or primarybody of the resonant structure 122. The projections 124 may bepositioned along the main body at midpoints between respective pairs ofsupport structures 126. FIG. 14 depicts the frequency spectrum of thedevice 120. The quality factor, Q, is 27,116. Other performanceimprovements may also be achieved via the device design shown in FIG.13, including, for instance, power handling levels of about 1-2 mV.

In one aspect of the disclosure, the disclosed resonator devices mayinclude support structures placed at nodal points of a resonantstructure in a symmetrical arrangement. Supporting the resonantstructure at the nodal points may configure the resonant structure forvibration at a high, overtone resonant mode, such as the 15th overtone(16th harmonic) of the fundamental resonant frequency. Such high mode,overtone operation is not limited to the above-described free-free beamresonator examples.

While the present invention has been described with reference tospecific examples, which are intended to be illustrative only and not tobe limiting of the invention, it will be apparent to those of ordinaryskill in the art that changes, additions and/or deletions may be made tothe disclosed embodiments without departing from the spirit and scope ofthe invention.

The foregoing description is given for clearness of understanding only,and no unnecessary limitations should be understood therefrom, asmodifications within the scope of the invention may be apparent to thosehaving ordinary skill in the art.

What is claimed is:
 1. A micromechanical device comprising: a substrate;a plurality of support structures anchored to the substrate; amicromechanical structure supported by the substrate via the pluralityof support structures and configured for overtone resonant vibrationrelative to the substrate, the overtone resonant vibration having a setof nodal points along the micromechanical structure; and a plurality ofelectrodes supported by the substrate and spaced from themicromechanical structure by respective gaps, the plurality ofelectrodes comprising multiple drive electrodes configured relative tothe micromechanical structure to excite the overtone resonant vibrationwith a differential excitation signal, and further comprising multiplesense electrodes configured relative to the micromechanical structure togenerate a differential output from the overtone resonant vibration;wherein: the plurality of support structures are coupled to themicromechanical structure between ends of the micromechanical structure;each support structure of the plurality of support structures isdisposed at a respective nodal point of the set of nodal points; themultiple drive electrodes comprise a positive drive electrode and anegative drive electrode; and the multiple sense electrodes comprise apositive sensing electrode and a negative sensing electrode.
 2. Themicromechanical device of claim 1, wherein the ends of themicromechanical structure are free ends.
 3. The micromechanical deviceof claim 1, wherein the plurality of support structures are disposed onopposing sides of the micromechanical structure, each side extendingalong a lateral dimension of the micromechanical structure.
 4. Themicromechanical device of claim 3, wherein the lateral dimension is alength of the micromechanical structure.
 5. The micromechanical deviceof claim 3, wherein the opposing sides are oriented in parallel with oneanother such that the micromechanical structure is beam-shaped.
 6. Amicromechanical device comprising: a substrate; a plurality of supportstructures anchored to the substrate; a micromechanical structuresupported by the substrate via the plurality of support structures andconfigured for overtone resonant vibration relative to the substrate,the overtone resonant vibration having a set of nodal points along themicromechanical structure; and a plurality of electrodes supported bythe substrate and spaced from the micromechanical structure byrespective gaps, the plurality of electrodes comprising multiple driveelectrodes configured relative to the micromechanical structure toexcite the overtone resonant vibration with a differential excitationsignal, multiple sense electrodes configured relative to themicromechanical structure to generate a differential output from theovertone resonant vibration, or both the multiple drive electrodes andthe multiple sense electrodes; wherein: the plurality of supportstructures are coupled to the micromechanical structure between ends ofthe micromechanical structure; each support structure of the pluralityof support structures is disposed at a respective nodal point of the setof nodal points; and the micromechanical structure is not supported atone or more of the set of nodal points; the plurality of supportstructures are disposed on opposing sides of the micromechanicalstructure, each side extending along a lateral dimension of themicromechanical structure; each support structure of the plurality ofsupport structures on a first side of the opposing sides is aligned withanother support structure of the plurality of support structuresdisposed on a second side of the opposing sides.
 7. The micromechanicaldevice of claim 1, wherein the overtone resonant vibration is at anovertone resonant frequency for the third overtone of a fundamentalresonant frequency of the micromechanical structure.
 8. Themicromechanical device of claim 1, wherein the overtone resonantvibration is at an overtone resonant frequency for the seventh overtoneof a fundamental resonant frequency of the micromechanical structure. 9.The micromechanical device of claim 1, wherein the overtone resonantvibration is at an overtone resonant frequency for the 15th overtone ofa fundamental resonant frequency of the micromechanical structure. 10.The micromechanical device of claim 1, wherein the overtone resonantvibration is at an overtone resonant frequency for the 31st overtone ofa fundamental resonant frequency of the micromechanical structure. 11.The micromechanical device of claim 1, wherein each support structure ofthe plurality of support structures has a length substantially less thana quarter-wavelength of a harmonic frequency of the overtone resonantvibration.
 12. A micromechanical device comprising: a substrate; aplurality of support structures anchored to the substrate; amicromechanical structure supported by the substrate via the pluralityof support structures and configured for overtone resonant vibrationrelative to the substrate, the overtone resonant vibration having a setof nodal points along the micromechanical structure; and a plurality ofelectrodes supported by the substrate and spaced from themicromechanical structure by respective gaps, the plurality ofelectrodes comprising multiple drive electrodes configured relative tothe micromechanical structure to excite the overtone resonant vibrationwith a differential excitation signal, multiple sense electrodesconfigured relative to the micromechanical structure to generate adifferential output from the overtone resonant vibration, or both themultiple drive electrodes and the multiple sense electrodes; wherein:the plurality of support structures are coupled to the micromechanicalstructure between ends of the micromechanical structure; each supportstructure of the plurality of support structures is disposed at arespective nodal point of the set of nodal points; and themicromechanical structure is not supported at one or more of the set ofnodal points; at least one of the multiple drive electrodes and at leastone of the multiple sense electrodes is disposed between each pair ofadjacent support structures of the plurality of support structures. 13.A micromechanical device comprising: a substrate; a plurality of supportstructures anchored to the substrate; a micromechanical structuresupported by the substrate via the plurality of support structures andconfigured for overtone resonant vibration relative to the substrate,the overtone resonant vibration having a set of nodal points along themicromechanical structure; and a plurality of electrodes supported bythe substrate and spaced from the micromechanical structure byrespective gaps, the plurality of electrodes comprising multiple driveelectrodes configured relative to the micromechanical structure toexcite the overtone resonant vibration with a differential excitationsignal, multiple sense electrodes configured relative to themicromechanical structure to generate a differential output from theovertone resonant vibration, or both the multiple drive electrodes andthe multiple sense electrodes; wherein: the plurality of supportstructures are coupled to the micromechanical structure between freeends of the micromechanical structure; each support structure of theplurality of support structures is disposed at a respective nodal pointof the set of nodal points; the micromechanical structure is notsupported at one or more of the set of nodal points, and each supportstructure of the plurality of support structures is laterally alignedwith another support structure of the plurality of support structures.14. The micromechanical device of claim 13, wherein the plurality ofsupport structures are disposed in a symmetrical arrangement along themicromechanical structure.
 15. The micromechanical device of claim 14,wherein the symmetrical arrangement divides the set of nodal points intoan equal number of supported and unsupported nodal points.
 16. Themicromechanical device of claim 13, wherein the plurality of supportstructures are disposed on opposing sides of the micromechanicalstructure.
 17. The micromechanical device of claim 13, wherein theovertone resonant vibration is at an overtone resonant frequency for thethird overtone of a fundamental resonant frequency of themicromechanical structure.
 18. The micromechanical device of claim 13,wherein the overtone resonant vibration is at an overtone resonantfrequency for the seventh overtone of a fundamental resonant frequencyof the micromechanical structure.
 19. The micromechanical device ofclaim 13, wherein the overtone resonant vibration is at an overtoneresonant frequency for the 15th overtone of a fundamental resonantfrequency of the micromechanical structure.
 20. The micromechanicaldevice of claim 13, wherein the overtone resonant vibration is at anovertone resonant frequency for the 31st overtone of a fundamentalresonant frequency of the micromechanical structure.